Perhaps time as we understand it on earth does not exist, but time in the universe does exist. Everything progresses as time goes by. Seconds or minutes are just measurments that are made-up to help us measure and understand time better.
However, you can bend it. A text I found in Wiki:
"In theory, and to make a clearer example, time dilation could affect planned meetings for astronauts with advanced technologies and greater travel speeds. The astronauts would have to set their clocks to count exactly 80 years, whereas mission control—back on Earth—might need to count 81 years. The astronauts would return to Earth, after their mission, having aged one year less than the people staying on Earth. What is more, the local experience of time passing never actually changes for anyone. In other words, the astronauts on the ship as well as the mission control crew on Earth each feel normal, despite the effects of time dilation."
Which leads to even more questions.
Conclusion: Time is a weird-ass thing, we'll never know what the truth actually is.